---------------------------lll_spect.C----------------------------





Usage:



	lll_spect ["ouput-file"] [dimension] [multiplier] [modulus]





Example:



	lll_spect "output.txt" 17 16907 2147483647





yields:



==============================================================

Modul:                  2147483647

Multiplikator:          16907

Dimension up to:          17

==============================================================

[dim]   [normalized_spectraltest]



2       0.339521

3       0.664031

4       0.563232

5       0.392962

6       0.55129

7       0.631505

8       0.743502

9       0.557965

10      0.687254

11      0.658881

12      0.754932

13      0.608785

14      0.48168

15      0.521614

16      0.558285

17      0.591849



Time [s]:       0









--------------------------------lll_search.C--------------------------



Usage:

        lll_search ["output-file"] [modulus] [prim-factors of modulus-1]



Example:

        lll_search "output-file" 2147483647 2 3 7 11 31 151 331





may yield:





2147483647 2 3 7 11 31 151 331

time    0       n       1       a       7       	0.000141999

time    0       n       5       a       16807   	0.337513

time    0       n       17      a       52958638        0.523292

time    0       n       37      a       655382362       0.570646

time    0       n       79      a       776069971       0.625391

time    4       n       1061    a       291971947       0.628671

time    5       n       1429    a       2092178609      0.631823

time    10      n       2671    a       1241412670      0.651958

time    18      n       4573    a       365705751       0.677872



time    41      		a       365705751       0.677872







Therefore the best parameter for modulus m=2147483647 equals

 	   			         a=365705751 with

					 M_8 = 0.677872





The random search is performed using a starting primitive root

in our case pr=7. Further primitive roots are calculated via pr^n mod m.

The prime factors in the input are used for primitive root checks.





